Covid Sampling (Challenge)

**This is an interactive problem.** You are given the task of finding people infected with COVID-19 among the whole population. There are a total of $N^2$ people and they are standing in a $N \times N$ matrix, one person per cell. Formally, for each $i$ ($1 \le i \le N$) and $j$ ($1 \le j \le N$), let's denote $A_{i, j} = 1$ if the person standing in the $i$-th row and $j$-th column of the m